### What’s Tested on GRE Math

GRE Math is a bit like high school math, without some of the hardest parts: for instance, you don’t have to write proofs or show your work! Here’s a quick rundown of the GRE Math skills required to conquer the Quant section, along with some of our best GRE Math tips.

**GRE Math Rules to Memorize**

You can’t bring a cheat sheet to the GRE, so you’ll need to memorize a number of GRE Math rules. This list isn’t exhaustive, but it does cover the different types of basic math rules and operations you’ll need to know on test day. It *doesn’t* cover problem-solving skills—we’ll look at those in a moment.

**Arithmetic:**

- How to add, subtract, multiply, and divide positive and negative numbers
- How to round numbers
- How to use the order of operations (PEMDAS) to simplify a complicated expression

**Algebra:**

- How to simplify one or more equations and solve for the value of a variable or variables
- How to find the solutions of a quadratic equation, and how to create a quadratic equation by multiplying binomials

**Inequalities and Absolute Values:**

- The meanings of ‘inequality,’ ‘absolute value,’ and related terms
- How to graph absolute values and inequalities on a number line, and how to interpret what you see on a number line
- How to solve equations and simplify expressions containing one or more absolute values
- How to simplify an inequality and/or combine multiple inequalities together

**Functions, Formulas, and Sequences:**

- The definition of a function, such as f(x) = 2x, and how to use it
- The definition of a sequence, such as S
_{x}= S_{x-1}+ 3, and how to use it - How to find missing terms in a sequence

**Fractions and Decimals:**

- How to add, subtract, multiply, and divide fractions and decimals
- How to simplify a fraction
- How to simplify a complex expression containing multiple fractions and/or decimals
- How to convert back and forth between fractions and decimals

**Percents:**

- How to find a certain percent of a number
- How to find a number that is a certain percent higher or lower than another
- How to convert between percents, fractions, and decimals

**Ratios:**

- The ratio between two given numbers
- How to find unknown values, given information about their ratio with other values

**Divisibility:**

- The definitions of divisibility terms, such as ‘divisible,’ ‘divisor,’ ‘factor,’ ‘prime factor,’ ‘multiple,’ ‘integer,’ etc.
- How to find divisors, prime factors, and multiples of a number
- How to find the remainder when one number is divided by another
- How to determine whether one number is divisible by another
- Quick rules for divisibility (such as the rules for whether a number is divisible by 3 or 9)
- The relationship between divisibility and prime factors
- The first 10 prime numbers

**Exponents and Roots:**

- How to add, subtract, multiply, and divide various combinations of numbers and variables with exponents
- The rules about negative versus positive numbers and exponents
- How to find the square root of a given number
- The perfect squares up to 202

**Number Properties:**

- What happens when you add, subtract, multiply, and divide positive and negative numbers
- What happens when you add, subtract, multiply, and divide even and odd numbers
- Methods to find the units digit of a large unknown number

**Statistics:**

- The definitions of mean, median, range, mode, quartile, percentile, and standard deviation

**Geometry Rules for GRE Math**

Geometry gets its own section, because it involves a lot of rules! Make your geometry flashcards early in your GRE Math studies, and review them often. Here are the basics.

**Basic Triangles:**

- The area of a triangle
- Rules regarding the side lengths and perimeter of a triangle, and the relationship between angles and side lengths
- The definition and properties of isosceles and equilateral triangles
- The sum of the angles of a triangle

- The Pythagorean Theorem
- The ‘special right triangles’ which have integer side lengths, such as the 3-4-5 triangle
- The properties of 30-60-90 and 45-45-90 triangles

**Circles:**

- The relationship between the radius, diameter, circumference, and area of a circle

**Quadrilaterals:**

- Identifying different types of quadrilaterals
- The area and perimeter of a square, rectangle, and parallelogram

**Other Shapes:**

- How to break down a complex shape into smaller shapes to find its area or perimeter
- The relationship between the number of sides of a polygon and the sum of its angles
- How to find the volume and surface area of basic 3-dimensional figures
- How to find the area of the border surrounding another shape

**Coordinate Geometry:**

- How to draw points and lines in a plane based on their equations
- How to identify the approximate equation of a line or the coordinates of a point based on a graph
- How to use algebra to determine whether a particular point is on a particular line
- Which points appear in which quadrants of the coordinate plane

**GRE Math Problem-Solving Skills**

Knowing the rules is only the first part of mastering GRE Math. You’ll also need to learn certain methods for solving different types of problems—and how to recognize those problems in the first place. Here are a few of the most important problem-solving techniques for GRE Math.

**Overall GRE Quant Skills:**

- How to quickly predict whether you’re likely to get a problem right or wrong, so that you can decide whether to guess
- How to make quick, reasonable guesses on tough problems
- How often to look at the clock during each Quant section, and what to do if you’re behind on time

**Discrete Quant/Word Problems:**

- How to translate text into equations
- How to identify unknown values in a problem and turn them into variables
- Strategies for common specific types of word problems, such as overlapping sets, rates, weighted averages, and percent change
- How to translate a problem about rates and work into a rate/work/time equation
- How to translate a problem about parts and wholes into equations involving percents, fractions, decimals, and/or ratios
- How and when to use Smart Numbers to solve a Discrete Quant problem
- How and when to work backwards to solve a Discrete Quant problem
- How and when to test cases

**Quantitative Comparisons:**

- How to simplify the quantities and the given information
- How to choose appropriate cases
- Strategies to prove answer choice D

**Data Interpretation:**

**Polishing Your GRE Math Skills**

Memorizing math rules and mastering problem-solving strategies are starting points for GRE Math. However, even if two people know exactly the same list of math techniques, they can end up with very different GRE Math scores. The difference lies in what the GRE is *really* testing: executive reasoning skills.

“Executive reasoning” refers to the type of high-level thinking you use when you have to make tough decisions, quickly, with limited time and information. You’ll need to do that, over and over again, as you take the GRE! You don’t get to spend all the time you’d like on every GRE Math problem. You also don’t get to test out multiple approaches to each problem until you find the perfect one. You need to set priorities and make the strategic moves that will maximize your score—even though that sometimes means guessing on ones you might be able to get right.

Don’t think that memorizing math rules is the main goal of your GRE Math studies. You should also spend plenty of time doing problems. And when you do problems, at least some of the time, do them in **timed, random sets** and **use a timer while you practice**. Also, when you fill out your problem log, review problems that you spent too much time on, or where you picked an inefficient approach, even if you got them right in the end.

There are other GRE Math skills, too. One GRE Math skill is your ability to handle test anxiety and mental fatigue. GRE Math experts are those who improve their test-taking stamina ahead of time so that they won’t get worn out on test day. They also address test anxiety head-on, rather than ignoring it and hoping that it goes away! Check out our GRE anxiety reduction tips for some ways to do this yourself. The GRE Math section also tests focus: can you pay careful attention to every single problem and avoid missing details and making careless mistakes? Luckily, focus can be trained, and there are many ways to avoid careless errors on test day.

You might not need geometry and inequalities in graduate school or in your career. However, you’ll definitely need some of the core GRE Math skills: executive reasoning, decision-making, focus, attention, and the ability to stay relaxed under pressure. Studying GRE Math is a unique chance to push yourself, grow, and hone your skills. 📝

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**Chelsey Cooley is a Manhattan Prep instructor based in Seattle, Washington.** *Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. **Check out Chelsey’s upcoming GRE prep offerings here.*

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